Such a thing exists and is called a "house fan". Rather than a door, where pets and children might stumble into the moving blades, it is placed in aforementioned upstairs and pointed out. Hot air is sent out of the house, the interior pressure is lowered and cool air makes its way in through wherever it can.

If, though, the house is closed up tight because the air conditioner has been on, one must remember to open a window or door to allow ingress of air, or whole house fan will overheat and die.

Could this be used a front door 'welcoming' device for salesmen, Jehova's witnesses etc?

With the fans running at 'gentle breeze', the unwary double glazing / religion pusher approaches. Upon becoming aware of the visitor's purpose, the homeowner switches to 'assimilate': A large plastig bag drops behind the door as the fans spool up and the bag is quickly filled with unwelcome guest.